Using imagesc to show the relation between IPR VS ( \sigma vs E), problem with matrix

I calculated the IPR for quantum system. this resulted in an N x 1 vector.

For this IPR there is the related eigenstates and eigenvalues, so we have another the vector for the eigenvalues E, and there is the $/sigma$ values.<br/>

So there is different E & IPR vectors for each sigma.<br/>In the end we have the IPR Matrix (vector matrix for different sigma values), and E matrix (vector matrix for different sigma values) and the vector sigma.<br/> imagesc takes (vector,vector,matrix) or imagesc(E,sigma,IPR). but there is a problem, because E isn't a vector anymore. <br/> how do I solve this? or did I just not understand the imagesc command? the code is below.

I flatten E to try and solve this, but I dont know if this is the right solution.

I also tryed to add it layer by layer and hold it but it also doesnt seem to work

N = 2^9;
z = ones(N-1,1);
c = 1;
ranNum = diag(rand([N 1]));
Nsig = 10^2;
sigma = ones(Nsig,1).';
E = ones(Nsig,N);
IPR = ones(Nsig,N);

for j = 1:Nsig
    sigma(j) = 0.01 + 0.01*(j-1);
    H1 = c*(diag(z,1)+ diag(z,-1) + diag(1,N-1)+ diag(1,-N+1));
    V1 = sigma(j) * ranNum ;
    H = H1 + V1;
    [psi,~] = eig(H);
    E(j,:) = eig(H);
    P1 = abs(psi).^2;
    IPR(j,:) = sum(P1.^2);
    
    imagesc(E(j,:),sigma(j),IPR(j,:))
    colormap('turbo')
    colorbar
    xlabel('E')
    ylabel('sigma')
    h = colorbar;
    ylabel(h, 'IPR')
    hold on
    
end

Answer 1

[Image Analyst]

Try using drawnow; instead of hold on:

N = 2^9;
z = ones(N-1,1);
c = 1;
ranNum = diag(rand([N 1]));
Nsig = 10^2;
sigma = ones(Nsig,1).';
E = ones(Nsig,N);
IPR = ones(Nsig,N);
for j = 1:Nsig
    fprintf('j = #%d of %d.\n', j, Nsig)
    sigma(j) = 0.01 + 0.01*(j-1);
    H1 = c*(diag(z,1)+ diag(z,-1) + diag(1,N-1)+ diag(1,-N+1));
    V1 = sigma(j) * ranNum ;
    H = H1 + V1;
    [psi,~] = eig(H);
    E(j,:) = eig(H);
    P1 = abs(psi).^2;
    IPR(j,:) = sum(P1.^2);
    
    imagesc(E(j,:),sigma(j),IPR(j,:))
    colormap('turbo')
    colorbar
    xlabel('E')
    ylabel('sigma')
    h = colorbar;
    ylabel(h, 'IPR')
    %     hold on
    drawnow;
end